The concept of biological diversity has evolved from a simple count of species to more sophisticated measures that are sensitive to relative abundances and even to evolutionary divergence times between species. In the course of this evolution, diversity measures have often been borrowed from other disciplines. Biological reasoning about diversity often implicitly assumed that measures of diversity had certain mathematical properties, but most of biology?s traditional diversity measures did not actually possess these properties, a situation which often led to mathematically and biologically invalid inferences. Biologists now usually transform the traditional measures to the «effective number of species», whose mathematics does support most of the rules of inference that biologists apply to them. The effective number of species, then, seems to capture most (though not all) of what biologists mean by diversity.